Power extraction from tidal channels - Multiple tidal constituents, compound tides and overtides

Many candidate sites for tidal stream power extraction are tidal channels, and the power that can be generated from these sites will be directly related to the amplitude and phase of the principal tidal constituents driving flow through the channel. This paper investigates this interaction between energy extraction and tidal constituents, and also the effect that power extraction may have on harmonics of the principal constituents (i.e. compound tides and overtides). Firstly, the variation in power extraction and available power (defined as the fraction of extracted power removed by idealised tidal turbines) are investigated over a spring/neap tidal cycle using a simple theoretical model. Results from the model are used to derive analytical bounds to the variation in power at spring and neap tide. These bounds are shown to depend on the channels natural dynamic balance and are of practical importance to tidal stream device developers looking to supply power to the electricity grid. Secondly, changes in the higher harmonics in channel flow rate are investigated for deployments of tidal farm in channels of various length and geometry. Specifically, it is shown that in general if the turbines provide a uniform drag resistance to the flow through the channel, even harmonics in the flow rate will decay with power extraction (leading to a more symmetric tide), whilst odd harmonics in the flow rate may decay or increase depending on the natural tidal dynamics. These variations can have significant effect on residual flows and the local environment. Throughout the paper results from the theoretical model are compared with a complex numerical model of energy extraction from the Pentland Firth. Good agreement is shown in all cases.